Isotope separation by magnetic fields

ABSTRACT

One of the isotopes of an element having several isotopes can be separated from the others in a dense, neutral plasma. Thus initially a neutral plasma is prepared including the element in question. This may consist of positive ions and negative electrons or alternatively of positive and negative ions, or else of a mixture of positive ions, negative ions and electrons. The plasma may then be injected into a magnetic field or may be generated in the field where more energy is imparted to a selected isotope than to the others. Finally, the isotopes are separated from each other on the basis of their differential energies. For example, the selected isotope may be given more energy than the others by stimulating it within the plasma at its resonant frequency which may be close to the cyclotron frequency, either by an electric field or by a magnetic field. In order to excite the other isotope, a different resonant frequency is required which depends on the plasma density, the relative concentration of electrons if the plasma contains electrons, the strength of the magnetic field, the ratio of charge to mass of the isotope, and possibly on the physical parameters of the plasma apparatus itself, such as the ratio of the length of the plasma column to its radius. The more energetic isotope may be separated by energy dependent chemical reactions, it may be collected by a positively biased probe or else the isotopes may be separated from each other by magnetic fields or in various other ways.

This is a division, of application Ser. No. 562,993, filed Mar. 27,1975.

BACKGROUND OF THE INVENTION

This invention relates generally to the separation of isotopes from eachother and particularly relates to a more inexpensive way for separatingisotopes in a substantially neutral, dense plasma.

Presently the principal means for separating uranium isotopes on acommercial basis is the gaseous diffusion process. In order to increasethe capacity of such diffusion plants a heavy capital investment isrequired which may be on the order of many hundred million dollars peryear.

On the other hand, in recent years research in many countries and bymany people has produced a vastly superior knowledge and insight thenature of plasmas. Particularly, our knowledge of the behavior of denseplasma has been much increased. Isotope separation in a dense plasmashould permit the separation of much larger quantities of the desiredisotopes at much lower cost and with less expenditure of energy.Furthermore, separation of isotopes in a dense plasma is facilitated bythe fact that plasma devices exist which can be used for similarprocesses. Among these devices are the so-called Q-machines.

It is well known that a beam of charged particles cannot exceed acertain density because the charged particles tend to repel each other.On the other hand, in a neutral plasma no matter how dense, individualcharged particles are neutralized by other particles of opposite charge.Therefore, a plasma can be made much denser than a charged beam.

It will be evident that a less expensive method for separating isotopeswill make it possible to utilize isotopes for purposes which in the pasthave simply been too expensive. For example, such isotopes may have manyuses in medicine. They may also be useful for light sources generatingmonochromatic light, that is light generated by a single isotope of asuitable element. Similarly, it may be desirable to manufacture laserscontaining as a laserable material a single isotope of a suitableelement. Single isotopes may also be used for nuclear reactors. In thiscase it may be desirable to utilize a special isotope which has the bestneutron properties for the reactor such as an especially large or smallneutron absorption cross-section.

Various methods have been suggested in the past for separating isotopesbesides the gaseous diffusion process. Among these methods are the useof a laster for exciting a particular energy level of one isotopewithout exciting the other isotopes. This may require a tunable laserfor optically exciting say the uranium isotope 235 preferentially overthe 238 uranium isotope. The excited uranium atom may now be morereadily ionized as distinguished from the unexcited ion so that aseparation of the charged and neutral isotopes can easily be carriedout. Such a separating method has been described, for example, in theU.S. Pat. to Pressman No. 3,558,877. A similar two photon scheme forexciting and subsequently ionizing a selected isotope has been describedin the U.S. Pat. to Levy et al. No. 3,772,519. The use of a laser tocause ionization of gas by the electric field caused by a focused laserbeam has been disclosed in the U.S. Pat. to Brubaker et al. No.3,478,204.

Also, the use of laser beams for the formation of plasma or forbombarding microparticles has been suggested in the U.S. Pat. to Vali etal. No. 3,360,733 and Hansen et al. No. 3,679,897.

Plasma confining devices having magnetic mirrors are well known in theart. An example of such a U.S. Pat. is the patent to Delcroix et al. No.3,257,579. The use of a diverging magnetic field, sometimes called amagnetic nozzle, has been proposed for the separation of at least twoisotopes in the U.S. Pat. to Roehling No. 3,845,300.

Finally, reference is made to a paper by Hidekuma et al. which appearsin Physical Review Letters of Dec. 23, 1974, Volume 33, No. 26, pages1537 -1540. This paper proposes to plug or retain desired ion speciesand permit the others to escape from a container. This is effected by amagnetic cusp created by suitable magnetic fields. The purpose of theexperiment was to permit impurities contained in the reactor to escapewhile retaining the desired particles.

It is therefore an object of the present invention to provide a novelmethod of and apparatus for the separation of isotopes of variouselements which is substantially less expensive than presently knownmethods.

Another object of the present invention is to provide a novel processfor separating isotopes making use of a plasma of relatively largedensity, thereby increasing the yield of such a method.

A further object of the present invention is to provide a method of andapparatus for separating isotopes which is applicable to many elementshaving more than one isotope.

SUMMARY OF THE INVENTION

The method in accordance with the present invention comprises basicallythree steps. Initially, a substantially neutral, dense plasma isgenerated including the isotopes in question. For example, the plasmamay consist of positive ions which are neutralized by electrons. On theother hand, it may be necessary to generate negative ions including theisotopes to be separated. In that case, the plasma must be neutralizedby suitable positive ions. Finally, a neutral mixture of positive andnegative ions and electrons may be used. The next step is to inject thisneutral, dense plasma into a magnetic field where one of the isotopes isgiven more energy than the others. It should be emphasized, however thatit is also feasible to generate the plasma in the magnetic field so thatit does not have to be injected. The differential energy may, forexample, by imparted by selectively driving the desired isotope at itsresonant frequency which is close to, but different from the cyclotronfrequency of the isotope. The corresponding collective resonantfrequency of the majority isotope species may, however, differsubstantially from its own particular cyclotron frequency. Thecollective resonant frequencies will generally depend on the plasmadensity, the relative concentration of electrons if the plasma containselectrons, the strength of the magnetic field, the ratio of charge tomass of the particular isotope and probably on the physical parametersof the plasma apparatus itself such as the ratio of the plasma columnlength to its radius. Finally, the selected isotope is separated fromthe others on the basis of their differential energies. This may, forexample, consist of a differential diffusion of the ions across amagnetic field, or magnetic mirrors may be utilized which confine themore energetic species. Many other ways will be discussed hereinafterfor separating one isotope from the other on the basis of theirdifferential energies, including energy dependent chemical reactions.Also, many ways will be discussed hereinafter for generating therequired plasma and for imparting differential energies to the variousisotopes.

The novel features that are considered characteristic of this inventionre set forth with particularity in the appended claims. The inventionitself, however, both as to its organization and method of operation, aswell as additional objects and advantages thereof, will best beunderstood from the following description when read in connection withthe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1a is a schematic cross-sectional view through a conventionalQ-machine which has been modified to separate potassium isotopes fromeach other, utilizing an oscillating magnetic field to generateinductively an oscillating electric field;

FIG. 1b is a cross-sectional view on enlarged scale of the probe whichmay be utilized with the apparatus of FIG. 1a and also depicting thepaths of an ion and an electron;

FIG. 2 is a schematic cross-sectional view of another modified Q-machineutilizing an oscillating electric field for separating the isotopes of adesired element from each other;

FIG. 3 is a schematic cross-sectional view of another apparatusembodying the present invention and including a plurality of magneticcoils for generating a rippling or varying magnetic field, thereby toimpart differential energy to ions moving along the longitudinal axis ofthe tube;

FIG. 4 is a chart plotting the magnetic field of the apparatus of FIG. 3as a function of distance to illustrate the ripples or undulations ofthe field as seen by a moving ion;

FIG. 5 is a cross-sectional view of apparatus similar to that of FIG. 3for generating a helical perturbing magnetic field which may also beused for the separation of isotopes;

FIG. 6 is a schematic cross-sectional view of apparatus providingadjacent magnetic fields with field-free spaces therebetween to causedifferential diffusion of desired isotopes, thereby to separate theisotopes from each other;

FIG. 7 is a schematic sectional view illustrating the behavior ofparticles in the device of FIG. 6 to illustrate the differentialdiffusion;

FIG. 8 is a schematic cross-sectional view illustrating a tube providedwith magnetic mirrors at both ends to effect diffusion of a lessenergetic isotope therethrough while retaining the more energeticisotope;

FIG. 9 is a schematic cross-sectional view of another machine showingmultiple magnetic mirrors to illustrate the differential diffusion ofisotopes through the device for the purpose of separating them;

FIG. 10 is a cross-sectional view of apparatus providing a magneticnozzle for generating a diverging magnetic field for the purpose ofseparating isotopes in accordance with their energy;

FIG. 11 is a cross-sectional schematic view of yet another apparatus forseparating isotopes from each other on the basis of their differentialvelocities due to an electric field resulting in a differential time offlight;

FIG. 12 is a chart illustrating a set of pulses used for acceleratingthe ions of the plasma and another set of pulses for separating the ionsin accordance with their differential time of flight;

FIG. 13 is a cross-sectional schematic view of another apparatus inaccordance with the present invention for separating isotopes by meansof the synchronous wave pressure generated by a steady magnetic fieldand an oscillating helical magnetic field;

FIG. 14 is a schematic cross-sectional view of apparatus for separatingisotopes by means of ion acoustic wave trapping; and

FIG. 15 is a schemtic cross-sectional view of apparatus forpreferentially scattering ions on the basis of their mass bycollisionless shocks.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

As explained hereinabove, the separation or enrichment of a selectedisotope requires basically three different and consecutive steps: In thefirst place it is necessary to create a plasma which is substantiallyneutral and relatively dense. The density of the plasma should be on theorder of 10¹⁰ to the order of 10¹² particles per cubic centimeter. Theplasma may either consist of positive ions neutralized by electrons orof negative ions neutralized by a suitable positive ion. Alternatively,the plasma may consist of a mixture of electrons and negative ions whichis neutralized by positive ions. The ions may either consist of theelement to be separated or else of a chemical compound containing theelement to be separated.

As the next step in the process it is now necessary to impart adifferential energy to the isotopes to be separated. This can beeffected in many ways which will subsequently be discussed. For example,the minor isotope, that is the isotope which is rarer, may be given moreenergy than the major isotope. Many ways will be described hereinafterhow this can be accomplished.

As the last step the two isotopes having previously acquired adifferential energy are now separated on the basis of their differentialenergies. Again, this can be accomplished in many different ways whichwill be discussed hereinafter.

Before discussing the equipment and the methods of the invention forimparting differential energies to the isotopes the generation of theplasma will now be described.

GENERATION OF A DENSE, NEUTRAL PLASMA

One of the simplest cases is the generation of a plasma consisting of analkali metal. Thus a plasma consisting of potassium can be readilygenerated in the following manner. The potassium is heated in a suitablefurnace in an evacuated space. The potassium atoms or the beam ofpotassium is now directed toward a hot electrode which may, for example,consist of tunsten, tantalum or rhenium. When a potassium atom impactsupon the hot electrode it will be ionized to create a positive potassiumion. Electrons are continuously emitted by the hot electrode. Theseelectrons neutralize the ions formed. The number of electrons depends onthe electric field generated by the ions which in turn is a function oftemperature.

Instead of evaporating potassium it is also feasible to start withpotassium chloride which is then sufficiently heated to break themolecular bond and hence to generate some neutral potassium atoms,chlorine atoms as well as potassium and chlorine ions. The process canthen be continued as described before.

Many other methods are readily available for generating a plasmacontaining the other alkali metals. Such a plasma can either begenerated within a steady longitudinal magnetic field in the manner of aQ-machine or else the plasma can be subsequently introduced into themagnetic field. This latter process may, for example, be necessary wherethe hot element is generated by filaments. The filaments can be spreadout outside of the magnetic field to provide sufficient space betweenadjacent filaments.

One method of separating the isotope ⁴¹ K is a chemical separationmethod. The K+ can be generated in a plasma as just described. Thefollowing reaction is endothermic and proceeds with the more energeticone of the isotopes.

    .sup.41 K+ + CF.sub.4 →.sup.41 KF + CF.sub.3.sup.+  (1)

now the potassium fluoride can readily be separated by a chemicalprocess.

Similarly the chlorine isotope ³⁷ Cl can be prepared from a neutralplasma containing K+. For example, carbon tetrachloride may be added tothe plasma and the following reaction takes place.

    e.sup.- + CCl.sub.4 →CCl.sub.3 + Cl.sup.-           (2)

Subsequently CH₃ Br is added which in turn will cause formation of CH₃Cl and the following reaction takes place.

    Cl- + CH.sub.3 Br→CH.sub.3 Cl + Br.sup.-            (3)

Reaction (3) is exothermic and can be used to separate ions on the basisof their energies. Thus if the chlorine isotopes of mass 35 and 37 aredifferentially heated so that chlorine 37 becomes less energetic, thereaction proceeds only with ³⁷ Cl⁻. A similar reaction takes place withCH₃ F.

A plasma containing uranium will generally have to be generated in asimilar manner. For example, the uranium may be separated as follows:

    U.sup.+ + AB→UA + B.sup.+                           (4)

in the above reaction A stands for fluoride, chlorine, nitrogen, oxygen,carbon and the like.

In case the reaction is endothermic, the separation can be effected byselectively heating the ion of the desired isotope. On the other hand,if the reaction is exothermic the production of the desired isotope ionis obtained by selectively heating the remaining species of the isotope.

It is also feasible to utilize selective reactions on the basis of therespective cross-sections which depend on energy. This is true evenwhere the energy thresholds for the reaction are not important.

Another approach which is more promising is to carry out selectivereactions using negative ions generated from UF₆ (uranium hexafluoride)which is a volatile uranium compound. Uranium hexafluoride has arelatively high vapor pressure at room temperature amounting to 100 tor.Further, uranium hexafluoride has a high electron attachment energy andhence readily forms negative ions.

For example, the following reaction will take place:

    UF.sub.6 + e→UF.sub.5.sup.- + F,                    (5)

where UF₅ is uranium pentafluoride.

In this case it will be noted that instead of a positive ion a negativeion is generated which now must be neutralized by a suitable positiveion such as K+.

The uranium pentafluoride ion may undergo an exothermic electrontransfer reaction with the uranium hexafluoride as follows:

    UF.sub.5.sup.- + UF.sub.6 →UF.sub.6.sup.- + UF.sub.5 (6)

the uranium isotope ion may now be separated, for example, by means of adissociation caused by a suitable collision of the energetic moleculecontaining the desired isotope in the following manner:

    UF.sub.6.sup.- + Xe→UF.sub.6-n.sup.- + nF + Xe,     (7)

where n stands for an integer smaller than 6. Again a chemicalseparation may be carried out. Instead of causing the uraniumhexafluoride to impact with xenon it is also feasible to use argon orsome other noble gas for the collisions, or even inert particles.

It is also feasible that the uranium pentafluoride ion undergoes thefollowing reaction with BF₃.

    uf.sub.5.sup.- + bf.sub.3 →uf.sub.4 + bf.sub.4.sup.-(8)

another reaction which may be used produces the formation of UF₅ CN⁻ inthe following manner:

    UF.sub.6.sup.- + HCN→UF.sub.5 CN.sup.- + HF         (9)

other chemical changes with uranium which permit the chemical separationof one isotope from another involves similar compounds of uranium withanother halogen such as chlorine, bromine or iodine. For example, thefollowing reaction may take place:

    UCl.sub.4 + Xe→UCl.sub.3 + Cl                       (10)

It will be understood that again other noble gases or inert particlesmay be used for the dissociation process, as well as other compounds ofuranium and chloride such as uranium hexachloride.

Selective charge exchange may also be carried out with other atoms ormolecules. In this case the reaction should be carried out on the basisof energy.

It is possible that an electron exchange takes place between the twoisotopes 235 and 238 of uranium hexafluoride. By selecting a suitableenergy the reaction may take place in a desired direction.

A neutral plasma containing both negative uranium ions and positive ionsmay involve the following reaction.

    Cs + UF.sub.6 →Cs+ + UF.sub.6 -                     (11)

this will directly produce the desired plasma which is neutral. Thisreaction may take place by direct contact of the two vapors. Theattachment energy for adding an electron to the uranium hexafluoride is4eV (electron volts). Similarly, 3.8 eV are required to remove anelectron from the cesium. The above reaction including cesium involves acharge transfer. Reactions of this type typically have largecross-sections because they can take place at large separations. Thusthis type of reaction can be expected to compete favorably against otherreactions such as:

    Cs + UF.sub.6 →Cs F + UF.sub.5.                     (12)

the latter reaction requires contact between the molecules. Otherreactions involving cesium are also feasible.

IMPARTING DIFFERENTIAL ENERGY TO THE ISOTOPES

As explained hereinbefore, the second step in the method of the presentinvention is to impart differential energy to the isotopes of aparticular element. This may, for example, be effected by making use ofthe collective resonance near the cyclotron frequency of the isotope inquestion. Since this process takes place in a relatively dense plasma,the cyclotron frequency is modified by the effects of the number ofparticles in the plasma, the strength of the magnetic field, the ratioof the electric charge to the mass of the isotope and other factors suchas the physical dimensions of the plasma. The electric charge separationof the plasma components may cause the collective resonant frequency ofthe major isotope to depart substantially from its own cyclotronfrequency. At the same time it will also depart from the collectiveresonant frequency of the minority isotope which now is somewhat closerto its own particular cyclotron frequency. The net result of thesecollective resonant separation effects or charge separation effects maycause the further enhancement of that portion of the resonant frequencyseparation which is due to differences in the ion cyclotron frequencyalone. It may also minimize the effect of the major species resonancealtogether because of variations of this frequency in different regionsof the plasma. The latter effect is one of several that may induce whatis sometimes referred to as resonance broadening.

Differential excitation of one isotope in the case of potassium will nowbe explained in connection with FIGS. 1a and 1b.

FIG. 1b illustrates, by way of example, a particular probe and will besubsequently discussed.

FIG. 1a illustrates a conventional, but modified, Q-machine which may,for example, consist of a cylindrical envelope 10 closed at both ends byend plates 11 and which may have a side tube 12 for connecting the tubeto a vacuum pump and other auxiliary equipment.

About the tube 10 are disposed coils 14 which may be annular and whichsurround the tube 10. The coils 14, when energized, generate a steadylongitudinal magnetic field. As shown at 15, the coils at both ends arecloser together to generate a denser magnetic field, usually known as amagnetic mirror.

The potassium may be evaporated from an oven shown schematically at 16and which may be maintained at a temperature on the order of 250° C(centigrade). The evaporated potassium then hits a hot plate 17 whichmay be maintained at a temperature on the order of 2,000° C. The plate17 may be heated by a filament 18, the power supply for which has notbeen illustrated for the sake of clarity.

The relative temperatures of the oven 16 and the hot plate 17 determinethe ratio of electron emission to potassium ion production. In otherwords, a potassium atom which hits the hot plate 17 will loose anelectron to generate a positive potassium ion. Electrons arecontinuously emitted due to the thermionic effect of the hot plate. Thehot plate may consist, for example, of tungsten, tantalum or rhenium.The ions and electrons which now make up a dense neutral plasma movetoward the left of FIG. 1a in accordance with their thermal velocitiesand pass through a circular opening 21 in a shield 20. The plasma mayhave a density of 10¹⁰ to 10¹² particles per cubic centimeter. Thepressure may be about 10⁻² to 15⁴ atmosphere and the temperature between1000° and 20,000° C.

Accordingly, the plasma proceeds toward the left where it is collectedby a collector 22. The voltage of the plasma with respect to thecollector 22 may be between 0 and +3 volts depending on the temperaturesof the oven 16 and the hot plate 17. The voltage between the shield 20and the collector 22 may be on the order of +0.1 to +0.5 volts. Sincethe ions must extract the electrons from the hot plate 17, the plasmaitself may be at a positive voltage with respect to the plate 17 whichmay be considered to be at ground potential. There is also provided aprobe 25 disposed between the shield 20 and the collector 22 in the pathof the plasma for collecting the isotope which has acquired the higherenergy, in this case the potassium 41 isotope. A range of oscillationfrequency is possible with this device. This includes the collectiveresonant frequency of both ion species. While an isotope is beingresonantly driven or "heated" individual ions of the other isotope areperiodically energized and deenergized by the driving field. The netresult is a large fractional energy difference between the resonant andthe nonresonant ionized isotopes.

In the space between the shield 20 and the collector 22 there isprovided a coil 26 for generating another magnetic field through whichthe plasma passes. This is an oscillating magnetic field and may begenerated by connecting the coil 26 to an oscillation generator 27. Acapacitor 28 may be disposed in one of the leads connecting thegenerator 27 to the coil 26 to provide a series resonant circuit whichtends to oscillate at the frequency of the generator 27. The result isthat an oscillating inductive field is developed in a directiontransverse to the direction of travel of the plasma.

This will be more fully explained hereinafter.

The shield 20 operates as a heat shield to shield the walls of theenvelope 10 from the high temperature of the hot plate 17. By coolingthe walls of the envelope 10, a low vapor pressure can be maintained andhence a substantially neutral plasma is obtained.

Additionally, a refrigeration coil 30 may be provided within the tube 10and substantially along the entire length of the tube. The coil 30 maybe maintained at room temperature or below by cold water or may even berefrigerated.

Due to the effect of the oscillating electric field combined with thelongitudinal magnetic field and the thermal velocity of the ions, theions assume a helical path from right to left as viewed in FIG. 1a.

The probe 22 is illustrated in greater detail in FIG. 1b to whichreference is now made. It may, for example, include a cylindrical shield31 which may consist, for example, of tantalum. It is insulated by twoinsulating cylinders 32 and 33 which may, for example, consist ofalumina. A circular plate-like collector 35 is disposed within theshield 31 and below the outer edge 36 thereof.

Curve 37 illustrates the path of an electron which has a very smalltransverse motion and therefore cannot penetrate to the collector 35.Curve 38 shows the path of an ion which has a much larger transversemotion and hence is able to impact on the collector 35 over the edge 36of the shield 31. The collector 35 may be supported by a heater wire 40for outgassing it and may be insulated by an insulating rod 41. However,during isotope separation, the collector 25 should be maintained cold asis the collector 35 so that the captured ions will not evaporate again.Hence the collector 35 may be cooled in any conventional manner.

The effects of the motions of the ions and electrons in a plasma of thetype generated in the apparatus of FIG. 1a will now be explained. It maybe convenient to explain first the cyclotron motion to which a chargedparticle is subject under the influence of a magnetic field. Themagnetic force acts at right angles to the velocity of a chargedparticle. Thus the vectors of the force and of the velocity form anangle of 90°.

The cyclotron frequency is determined by the ratio of the charge to themass of the particle multiplied by the magnetic field and divided by thelight velocity. The Larmor radius is proportional to the square root ofthe particle energy divided by the cylotron frequency.

It is now possible to excite a charged particle by subjecting it to anoscillating electric field of a frequency close to but different fromthe cyclotron resonant frequency.

In this case there must be both a magnetic field and an electric fieldat right angles, the electric field having a component parallel to themotion of the particle. The frequency with which the electric fieldvaries should be such that the particle has an increase in energy orvelocity. Thus the particle is accelerated along a spiral or cycloidalpath. As a result, the particle has a translational velocity at rightangles to the electric field.

If the particle is driven by its own resonant frequency it will continueto gain energy. On the other hand, a particle or ion that is out ofresonance will vary its energy in a manner determined by the square of asine function. On the other hand, an ion which is in phase consistentlyincreases its energy according to the square of time. As a result, aparticle which is in resonance with the oscillating electric field willgain energy or will become "heated". The period of time may be soselected that there is a maximum difference on the average between theenergy of a particle in resonance and another particle which is not inresonance.

Thus it is feasible to excite one isotope which occurs as a smallpercentage of the total ionized isotope population at its collectiveresonant frequency which may be near the cyclotron resonant frequency.However, it should be realized that even in this case the collectiveresonant frequency which is different from the cyclotron frequency maybe close thereto. The other isotope is only heated when it is subjectedto its collective resonant frequency. The reason for the difference inbehavior between the two ion species is that the collective motions ofthe more abundant isotope induces electrical forces within the plasmadue to charge separation. This modifies the circular motion of the ionseffected by the steady magnetic field alone. On the other hand, themotions of the minor isotope causes much less charge separation andhence smaller electric fields and smaller shifts in the resonantfrequency. To a large extent charge separation due to the motion of theminor isotope is cancelled by an almost equal, but opposite, separationof the major isotope. This motion of the major species, however,involves little energy because only a small motion of the major speciesis required to balance the motion of the minor species.

A detailed account of this phenomenon, therefore, also depends uponspecific parameters of the plasma device. However, the followingquantitative expression is applicable to a plasma slab confined by thetwo unbounded plane surfaces. It serves to illustrate the most importantfeatures of this resonant frequency dependence upon collective ionmotions: ##EQU1## where l indicates the species of the chargedparticles; and ω_(pl) is the plasma frequency for the lth particle orassociated with the corresponding ion species which is determined asfollows: ##EQU2## In formulas (11) and (12): E_(x) is the electric fieldwithin the plasma slab in the direction perpendicular to the planarboundaries.

e is the charge of the electron

n_(l) is the number density of particles for the lth isotope or species

m_(l) is the mass of the lth isotope

Further, in equation (11)

ω_(cl) is the cyclotron frequency, for the lth species.

ω_(o) is the driving frequency

ν_(l) is the effective collision frequency for the lth species and i is√-1

If one sets the denominator of equation (11) equal to 0 the conditionfor resonance is obtained. This formula can now be simplified byassuming that a plasma of electrons, and ions of U235 and U238 ispumped. It is further assumed that pumping takes place at the resonantfrequency for U235 and that the collision frequency is much less thanthe difference in cyclotron frequencies for the two uranium isotopes.Then one obtains the following equation for resonance: ##EQU3##

In the above formula n_(j) is the desired number of species j and m_(j)is the mass of species j.

In the above formula ω_(p) again stands for the plasma frequency, thesubscript e stands for the electron and 235 and 238 indicate therespective values for the two uranium isotopes. In the above formulasfor simplicity the effects on the cyclotron frequency of molecularmasses instead of simple ions have been neglected. Assuming now that theion density n = 10¹¹, and B the magnetic field is 10⁴ gauss, thefollowing relation holds. ##EQU4## Accordingly, ω_(c235) = 40 B = 4 ×10⁵.

It should be noted that a steady longitudinal magnetic fieldsubstantially constrains the electrons but not the ions. In other wordsthe ions can assume a substantial transverse motion. Therefore, if theplasma consists of ions and electrons the electrons are contained in athin cylinder along the axis of the tube so that the electric chargesare generally neutralized. However, the ions are capable of makingtransverse excursions outside of this cylinder, particularly when theyare heated, that is when they have acquired energy.

The attraction exerted by the electrons on the positive ions tends toforce the ions back toward the axis of the tube. The transverse motionsof the major isotope result in a larger charge separation. This in partexplains why the collective resonant frequency is different fordifferent isotopes. In this case also the plasma should extend over agreater length so that the electrons cannot move axially out of theplasma and return along other field lines.

On the other hand, if the plasma consists of positive and negative ionsthen the plasma need not be of such great length. The isotope whichresonates with the applied oscillating frequency tends to assume agreater translational velocity and hence moves away further from theaxis. When the minor species is excited the motion of the major speciestends to be in the opposite direction and thereby compensates for thecharge separation. This effect can be used in accordance with thepresent invention for the separation of the isotopes. The differenttranslational velocity is made use of in the probe of FIG. 1b. Apotential may be applied to the collector 35 such that only the moreenergetic isotope is able to reach the collector.

The apparatus of FIGS. 1a and 1b has been successfully operated for theenrichment of both potassium and chlorine isotopes. The plasma in theapparatus of FIG. 1a consisted of a column 5 centimeters in diameter and1 meter long. The number of particles was between 10⁹ and 10¹⁰ per cubiccentimeter. The temperature of the ions and electrons corresponds to anenergy of 0.2 eV. The ion velocity was 7 × 10.sup. 4 centimeter persecond. The steady magnetic field was between 2 and 3.5 kilogauss (KG).The oscillating magnetic field was 15G or 30G peak-to-peak. The Larmorradius is 1.5 millimeter and the collective resonant frequency of theminor isotope is between 70 and 73.6 KHz.

Ions were observed which had an energy up to 3 eV when the plasma isdriven at the collective resonant frequency of ⁴¹ K. The currentobserved with the probe of FIG. 1b which may be viewed as an ion energyanalyzer was plotted as a function of the frequency of the oscillatingmagnetic field for various probe potentials. The shift between thecollective resonant frequencies of the two ion species increases as theplasma density is increased. The width of the resonant peak is on theorder of 2% which may be due to ion transit time broadening. It furtherincreases as the plasma noise level increases.

The enrichment factors can be computed by extrapolating the resonanceobtained for ³⁹ K symmetrically toward the ⁴¹ K resonances. From thisdata enrichment factors between 20% and 83% were found, depending on theretarding potential applied to the probe of FIG. 1b. The lower the probepotential, the higher the enrichment factor.

When the oscillating magnetic field is suddenly turned off it takesabout 1 millisecond for the energetic ions to disappear. This indicatesthat the observed resonances are bulk plasma resonances rather thanlocalized resonances near the probe. By increasing the pump power thecollection rate can be increased. Further, better resolutions can beachieved with higher magnetic fields because the difference frequencybetween the two resonant frequencies increases linearly with themagnetic field.

Similar results have been obtained with a mixture of K+, Cl- andelectrons. A separation between 35 Cl and 37 Cl was observed in themanner previously described.

The ions of a neutral plasma can also be excited or heated by apparatusdifferent from the illustrated in FIGS. 1a and 1b. Such apparatus isillustrated in FIG. 2 to which reference is now made. The apparatus ofFIG. 2 is again a modified Q machine and includes a closed container 45which may, for example, have a square or rectangular cross-section andthe container 45 may be closed by end plates 46. The ions may begenerated as shown schematically by the box 47 which may be identical tothe oven 16 and hot plate 17 in FIG. 1a. In any case, positive potassiumions or some other suitable ions issue from the box 47. They are nowaccelerated by an accelerator grid 48 to which a suitable negativevoltage is applied. A source of electrons must also be provided togenerate a neutral plasma. Such an electron source is well known andhence has not been illustrated.

A steady longitudinal magnetic field is generated in the container 45.This may, for example, be effected by the coils 50 surrounding thecontainer 45. A pair of conductive parallel plates 51 and 52 aredisposed on opposite sides in the container 45. An oscillation generator53 is connected to the plates 51 and 52 for developing an oscillatingelectric field at the desired resonant frequency as previouslyexplained. The oscillating electric field of the apparatus of FIG. 2serves the same purpose as does the oscillating magnetic field of theembodiment of FIG. 1a.

The ions will now travel due to their thermal motion from left to rightas viewed in FIG. 2 and may be collected by a probe 54 which may, forexample, take the form of the probe of FIG. 1b. The direction of thebeam is shown by the arrows 55. Otherwise, the embodiment of FIG. 2operates in the manner of that of FIG. 1 as previously explained.

In accordance with the present invention it is also feasible to impartenergy to a selected isotope in a different manner. This is illustratedin FIGS. 3 and 4 to which reference is now made. In the embodiment ofFIG. 3 it is assumed that uranium ions are introduced into the tube 57on the left-hand side as shown by arrow 58. Either positive or negativeions may be used. Negative uranium ions may be generated in the mannerpreviously explained. They are now accelerated by a pair of acceleratinggrids 60 to which a negative voltage for positive ions or a positivevoltage for negative ions is applied so that the accelerated ions movetoward the right. It will be understood that the plasma is neutralizedagain as previously explained by suitably charged ions or by electrons.

A rippling magnetic field is generated by a set of spaced coils 61, 62,. . . At the end of the tube a magnetic mirror is generated by the coil63. The magnetic configuration is illustrated in FIG. 4 where Bindicates the magnetic field and d the distance. As clearly shown by thecurve 64, the magnetic field is rippled or undulated.

As a result, an ion moving in the direction of arrow 58 sees undulatingor oscillating magnetic field lines which are equivalent to the effectof the apparatus of FIGS. 1a and 2. In other words, a moving ion sees anundulating magnetic field. If now the velocity of the ions is properlyrelated to the undulations of the magnetic field, the ions see aresonant frequency which may be the composite resonant frequency of thedesired isotope. A uniform longitudinal magnetic field is maintained inaddition by the coil 65, thereby to constrain the plasma in thedirection of the axis of tube 57.

A modification of the apparatus of FIG. 3 is shown in FIG. 5 whereinlike elements are designated by the same reference numbers. Theembodiment of FIG. 5 differs from that of FIG. 3 in that a set ofhelical coils 67 are provided. These helical coils will produce helicalmagnetic field lines to aid in propagating the uranium ions in thedirection of arrow 58. They will also promote a transverse motion of theions which will differ for the different isotopes, as explainedhereinabove, thereby to facilitate the eventual separation of theisotopes.

SEPARATION OF THE ISOTOPES

In the previous portion it has been explained how the isotopes of anelement can be differentially heated, that it can be made to assumedifferent energies. In the subsequent portion of this description itwill be explained how the isotopes of different energies can bephysically separated from each other to provide an isotope enrichment orseparation.

By way of example, this may be accomplished by the probe 22 of FIG. 1aor that of FIG. 1b. However, there are many other ways in which isotopescan be separated from each other on the basis of their differentialenergies. This may, for example, be effected by means of a source ofmagnetic barriers separated by field-free spaces which permits a morerapid diffusion of more energetic ions across a field-free space betweensuccessive magnetic fields. Such an embodiment of the invention isillustrated in FIGS. 6 and 7 to which reference is now made.

FIG. 6 illustrates schematically a closed container 70 in which suitablecoils are provided, not illustrated for the sake of clarity. Theygenerate a magnetic field B going in a downward direction as shown byarrow 71 and another magnetic field going in an upward direction asshown by arrow 72. The two magnetic areas are separated by a field-freespace 73. The symbols 74 indicate that the current in the coils flowsdownwardly while the symbols 75 indicate electric current in the coilsflowing upward from the paper plane.

FIG. 7 illustrates by way of example the path of an ion 76 as it entersthe space 77 having a downwardly directed magnetic field 71. Theparticle collides, as shown at 78, with another particle and its path ischanged to provide a downward spiral illustrated at 80. By subsequentcollisions such as shown at 81, the particle moves eventually into thefield-free space 73 and then into the second magnetic field space 82 andeventually emerges as shown at 83. The diffusion time of the particle 76depends on the Larmor radius which is the radius of the spiral 80. Eachcollision of the particle transports the orbit of the ion by up to thediameter of its helix such as 80.

It will be understood, of course, that as a result of each collision aparticle has roughly an equal probability of being moved toward the leftinstead of toward the right. However, for the sake of clarity only thosecollisions have been illustrated which are of interest here. A similarpath of a second, more energetic particle 84, is also depicted.

It should be noted that if collisions with neutral particles dominate sothat the scattering cross-section is only weakly dependent on energy,the more energetic species of ion will diffuse across the magneticspaces 77 and 82 more rapidly than the less energetic ions.

It is also feasible to use magnetic mirrors to confine the hotterspecies while the cooler or less energetic ions flow out of the mirrorspace. Such an embodiment of the present invention has been illustratedin FIG. 8 to which reference is now made.

FIG. 8 illustrates an apparatus comprising a container 90 which may beof circular cross-section and which should be closed at both ends, notshown. A suitable dense, neutral plasma including, for example, theuranium isotopes is introduced into the cylinder 90. A longitudinalmagnetic field is generated by the coils 91 surrounding the cylinder 90.Additional magnetic coils are provided at both ends as shown at 92 toprovide a magnetic mirror at both ends of the tube 90. The plasma, ofcourse, must be introduced into the magnetic space in the mannerpreviously described and the ions must be differentially heated.

The magnetic lines of force are shown schematically at 93. An energeticion is shown at 94 and its helical path.

As an ion moves into the mirror region its transverse motion builds upat the expense of its longitudinal motion. The effect is stronger thelonger the initial transverse motion. Hence, an ion which has beenheated in the transverse direction upon reaching the right-hand end isreturned toward the left as shown at 95, because it does not have enoughlongitudinal motion energy to pass through the mirror.

The path of a less energetic ion is shown at 96. Conversely because thision has less energy, it has less transverse motion and hencecomparatively speaking a larger longitudinal motion. Due ot its higherenergy in the longitudinal direction, it can escape the magnetic mirroras shown at 97. As a result, the less energetic ions escape the mirror,while the more energetic ions are confined by the two mirrors. This isone scheme for separating the energetic from the less energetic ions.

Instead of confining the plasma between two mirrors it is also feasibleto cause diffusion of the plasma through a multiplicity of mirrors. Sucha structure has been illustrated in FIG. 9. Again the plasma iscontained in a cylindrical tube 90 which may be closed at its far ends.A longitudinal magnetic field is generated by a coil 91 providing asteady field. The magnetic mirrors are provided by a plurality of spacedcoils 100. The resulting magnetic field lines are indicated at 101. Itwill be noted that the field lines converge at each of the mirror coils100. Accordingly, this structure will provide a differential diffusionof the less energetic ions through the multiplicity of mirrors 100. Onthe other hand, the more energetic ions tend to be retained by each ofthe magnetic mirrors in the manner previously explained.

Another method of separating isotopes on the basis of their differentialenergy may be effected by means of a so-called magnetic nozzle. As shownin FIG. 10, the plasma is introduced into an outwardly flared tube 105which generally has the shape of a trumpet or bell. The bell-shaped tube105 may again be of cylindrical cross-section and may be provided withspaced magnetic coils as shown at 106. The coil 107 has a largerdiameter to accommodate the shape of the bell-like tube 105. As aresult, the magnetic field lines 108 are outwardly curved to provide themagnetic nozzle. The path of an energetic particle is shown at 110. Itis characterized by a relatively large transverse velocity component. Atthe left-hand side of tube 105 the magnetic field is relatively high andis correspondingly lower on the right-hand side. Accordingly, theperpendicular velocity of the more energetic ion in the left-hand sideis converted to a more parallel velocity on the right-hand side as shownin 111. Accordingly, the more energetic particles are ejected basicallyat an angle to the longitudinal axis of symmetry.

On the other hand, a non resonant isotope, that is an isotope of lowerenergy, has the path shown at 112. It has a smaller transverse velocityas previously explained. The parallel or axial energy of the low energyions also increases toward the right of FIG. 10, but to a much smallerextent because the total energy, that is the parallel and transverseenergies, must be conserved. The different isotopes can be separated onthe basis of their axial energies as, for example, by using energyselective devices similar to those proposed for the direct energyconversion on mirror fusion devices. They may also be separated bysimply passing them through suitably biased grids. Spatial separation isalso possible. It is, of course, assumed that the ions have previouslybeen heated or given differential energies.

In general, the magnetic nozzle of FIG. 10 converts the energyperpendicular to the magnetic field lines of energetic isotopes intoenergy parallel to the magnetic field lines which can then be used toseparate the isotopes.

Alternatively, it is possible to separate the more energetic ions fromthe less energetic ions by their differential time of flight. This maybe accomplished with the apparatus of FIG. 11. The plasma is confinedagain in a tube 115 and the ions are differentially heated so that themore energetic ions move faster or have a higher velocity than that ofthe low energy ions. Actually, the ions may simply be acceleratedinitially by a pair of grids 116 arranged at the left-hand side of thetube 115. Suitable pulses are applied between the grids 116 by a pulsegenerator 117 and the pulses are illustrated in FIG. 2 at 118. Theduration of each pulse 118 and the off time are determined by thedesired velocity of the accelerated ions.

The velocity of the lighter ion is somewhat larger than that of theheavier ion so that the lighter ion will arrive first at a second pairof grids 120. A suitable decelerating voltage is now applied by thepulse generator 117 to the decelerating grids 120. These pulses areillustrated in FIG. 12 at 121 and are of the opposite polarity than thatof the acceleration pulses 118. These pulses are so timed with respectto the accelerating pulses 118 that they will permit a faster ion topass but will repel the slower ion. However, unless the duration of eachaccelerating pulse 118 is relatively short and the accelerating voltageis relatively low, the required length of tube 115 may be relativelylarge.

The isotopes may also be separated by utilizing the wave pressure of thecyclotron wave on the resonant isotope. In this case it may be desirableto include another gas besides uranium to facilitate the propagation ofthe cyclotron waves. This may be effected in the apparatus of FIG. 13.Here again the plasma is confined in a cylindrical tube 90. A series ofcoils 125 surrounds the tube 90 to generate a longitudinal magneticfield. A helical coil 126 is also disposed surrounding the tube 90 togenerate a helical field which is made to oscillate by connecting thecoils 126 to a suitable oscillation generator as shown in FIGS. 1a and2.

The steady magnetic field is indicated by the parallel arrows 127. Theoscillating magnetic field is indicated by the arrow 128. The resultingelectric field is shown at 130 which, of course, oscillates. Theparallel force vector is illustrated at 131 and the velocity of theparticle is shown at 132. A longitudinal force is exerted by thecyclotron wave on the ions. Those ions which are resonant are subjectedto a proportionately stronger force. This stronger force is sufficientto overcome an elastrostatic barrier shown schematically by the grids133 between which a voltage is applied by the voltage source 134. Thisnow makes it possible to separate by electric repulsion forming anelectric barrier the more energetic from the less energetic ions. Theso-called hotter ions escape toward the right while the other ions areconfined.

It is also feasible to make use of acoustic waves for trapping thefaster or lighter isotope. This is illustrated in FIG. 14 where again 90indicates a cylindrical tube in which the plasma is confined. Theacoustic wave is launched by the grids 140 to which an oscillatingvoltage is applied by a generator 141. This will create large amplitudeacoustic waves of the ions. The acoustic wave is shown schematically at142. The ions of the lighter isotope move faster and hence more nearlyat the velocity of the wave and thus may be trapped in the wave trough143 as shown at 144.

The plasma contains relatively hot electrons and relatively cold ions.The acoustic wave moves faster than the mean thermal speed of the ions.However, the lighter ions have a slightly higher thermal velocity andmove more nearly at the speed of the acoustic wave. Those ions moving atthe speed of the acoustic wave are trapped by the wave which movestowards the right. Hence more light ions are trapped. On the other hand,the less energetic ions are left behind.

Finally, as shown in FIG. 15, collisionless shock may be utilized forscattering the lighter ion while permitting the heavier ion to pass. Theplasma is contained in a container 90 divided into two regions 145 and146 by means of suitable closed grids or cages 145a, 146a respectively.The plasma containing uranium or some other isotope is containedessentially in the cage 145a. The two cages 145a and 146a which may, forexample, consist of wire grids, may be pulsed by a pulse generator 147which generates the pulses 148. Since the two cages now have differentpotentials a shock front is launched into one section shownschematically at 150. The shock front moves toward the left as shown byarrow 151. This shock front 150 preferentially scatters the lighter ionas shown at 152. The heavier ion shown by arrow 153 is relativelyunaffected and remains behind. Hence the lighter ion is preferentiallyconcentrated and collected at the left-hand end of the tube 90. Thepotentials of the two cages 145 and 146 determines in turn the plasmapotential.

There has thus been disclosed a method of and apparatus for separatingisotopes or enriching a desired isotope. This is accomplished in a denseneutral plasma. Various methods have been disclosed for generating sucha plasma consisting, for example, of alkali metals or uranium.Differential energies may be imparted to the isotopes, for example, byaccelerating them under an electric field so their velocity depends ontheir mass. Alternatively, differential energy may be imparted to theisotopes by subjecting them to a resonant frequency which differs foreach isotope. Finally, various devices have been disclosed forphysically separating or enriching the desired isotope on the basis oftheir different energies. This may, for example, be effected bydifferential diffusion through a magnetic field or magnetic mirrors orby utilizing a magnetic nozzle. Alternatively, a selected isotope may betrapped in an acoustic wave or the isotopes may be differentiallyscattered depending on their mass by collisionless shocks. Finally, thesynchronous wave pressure may be utilized for separating the isotopes.The energetic isotopes may also be separated from the less energeticisotopes by energy dependent chemical reactions as previously described.

What is claimed is:
 1. The method of separating one isotope of anelement from the others which comprises the steps of:(a) generating adense, substantially electrically neutral plasma including an elementhaving at least two ionized isotopes to be separated; (b) generating asubstantially steady magnetic field extending through the plasma andsubstantially parallel to a longitudinal axis; (c) imparting more energyto a selected isotope than to the other isotopes while the element is inthe magnetic field by subjecting the element to its resonant frequencydetermined by the plasma density, the strength of the magnetic field,and the ratio of the charge to the mass of the selected isotope, theplasma being large enough to encompass the orbital paths of theisotopes; (d) generating a second steady magnetic field; and (e)separating the isotopes from each other on the basis of theirdifferential energies by causing the isotopes which have receiveddifferent energies to diffuse across the second magnetic field, wherebythe isotopes having different energies will diffuse at different rates.2. The method of separating one isotope of an element from the otherswhich comprises the steps of:(a) generating a dense, substantiallyelectrically neutral plasma including an element having at least twoionized isotopes to be separated; (b) generating a substantially steadymagnetic field extending through the plasma and substantially parallelto a longitudinal axis; (c) imparting more energy to a selected isotopethan to the other isotopes while the element is in the magnetic field bysubjecting the element to its resonant frequency determined by theplasma density, the strength of the magnetic field, and the ratio of thecharge to the mass of the selected isotope, the plasma being largeenough to encompass the orbital paths of the isotopes; and (d)separating the isotopes from each other on the basis of their differentenergies by generating a plurality of spaced magnetic mirror fields inthe plasma region, thereby to confine the more energetic isotope whilepermitting the less energetic isotope to pass through the magneticmirror fields.
 3. The method of separating one isotope of an elementfrom the others which comprises the steps of:(a) generating a dense,substantially electrically neutral plasma including an element having atleast two ionized isotopes to be separated; (b) generating a steadymagnetic field along a longitudinal axis; (c) injecting the plasma intothe magnetic field; (d) moving the ionized isotopes by plasma expansionalong the longitudinal axis in a predetermined direction; (e) impartingmore energy to a selected isotope than to the other isotopes while theelement is in the magnetic field by subjecting the element to itsresonant frequency determined by the plasma density, the strength of themagnetic field, and the ratio of the charge to the mass of the selectedisotope, the plasma being large enough to encompass the orbital paths ofthe isotopes; and (f) separating the isotopes from each other bygenerating additional spaced magnetic fields substantially at rightangles to the longitudinal axis with a substantially field-free spacetherebetween, whereby the more energetic ionized isotope preferentiallymigrates long the longitudinal axis in the predetermined directionacross the magnetic fields and the field-free space therebetween.
 4. Themethod of separating one isotope of an element from the others whichcomprises the steps of:(a) generating a dense, substantiallyelectrically neutral plasma including an element having at least twoionized isotopes to be separated; (b) generating a steady magnetic fieldalong a longitudinal axis; (c) injecting the plasma into the magneticfield; (d) moving the ionized isotopes along the longitudinal axis in apredetermined direction; (e) imparting more energy to a selected isotopethan to the other isotopes while the element is in the magnetic field bysubjecting the element to its resonant frequency determined by theplasma density, the strength of the magnetic field, and the ratio of thecharge to the mass of the selected isotope, the plasma being largeenough to encompass the oribital paths of the isotopes; and (f)separating the isotopes from each other by generating two additionalmagnetic fields spaced from each other substantially normal to and alongthe longitudinal axis to provide spaced magnetic mirrors, whereby themore energetic ionized isotope tends to be confined by the mirrors whilethe less energetic isotope tends to pass the magnetic mirrors.
 5. Themethod of separating one isotope of an element from the others whichcomprises the steps of:(a) generating a dense, substantiallyelectrically neutral plasma including an element having at least twoionized isotopes to be separated; (b) generating a steady magnetic fieldalong a longitudinal axis, the steady magnetic field having field lineswhich diverge outwardly in the area of one end of the magnetic fieldfrom the longitudinal axis; (c) injecting the plasma into the magneticfield; (d) moving the ionized isotopes along the longitudinal axistoward the diverging field lines; (e) imparting more energy to aselected isotope than to the other isotopes while the element is in themagnetic field by subjecting the element to its resonant frequencydetermined by the plasma density, the strength of the magnetic field,and the ratio of the charge to the mass of the selected isotope, theplasma being large enough to encompass the orbital paths of theisotopes; and (f) separating the isotopes from each other by thediverging field lines, thereby to permit spatial separation thereof. 6.Apparatus for separating the isotopes of an element from each other in adense, substantially electrically neutral plasma comprising:(a) anelongated evacuated container having a longitudinal axis; (b) means forgenerating a dense, substantially electrically neutral plasma andinjecting it into said container and for propagating the ions along saidaxis in a predetermined direction; (c) means for imparting differentialenergies to the ionized isotopes by subjecting the element to itsresonant frequency; and (d) means for generating spaced magnetic fieldsin said container substantially at right angles to said longitudinaldirection, having a field-free space therebetween, whereby the moreenergetic ionized isotope will preferentially migrate across thetransverse magnetic fields and the field-free space.
 7. The method ofseparating one isotope of an element from the others which comprises thesteps of:(a) generating a dense, substantially electrically neutralplasma including an element having at least two ionized isotopes to beseparated; (b) generating a substantially steady magnetic fieldextending through the plasma and substantially parallel to alongitudinal axis; (c) applying an additional steady magnetic field tothe plasma varying periodically in magnitude along a predetermineddirection; (d) causing the ions of the element to be separated to movealong the predetermined direction and within the two magnetic fields sothat the ions experience variations of the resultant magnetic fieldcorresponding to the desired resonant frequency of a selected isotopedetermined by the plasma density, the strength of the resultant magneticfield, and the ratio of the charge to the mass of the selected isotope,the plasma being large enough to encompass the orbital paths of theisotopes; and (e) separating the isotopes from each other on the basisof their differential energies by providing along the predetermineddirection an additional magnetic field of such a magnitude to permitsubstantially all less energetic ions to pass along the predetermineddirection through the additional magnetic field while reflectingsubstantially all most energetic ions corresponding to the selectedisotope.
 8. The method defined in claim 7 wherein the additionalmagnetic field is helically perturbed to produce helical magnetic fieldlines, whereby the ions of the element to be separated are caused tomove through the magnetic field lines.
 9. Apparatus for separating theisotopes of an element from each other comprising:(a) an elongatedevacuated container; (b) means for generating a steady magnetic field insaid container having a longitudinal axis; (c) means for generatingspaced steady magnetic fields in said container along said longitudinalaxis; (d) means for generating a dense, substantially electricallyneutral plasma in said container and for injecting the resulting plasmainto the magnetic field; (e) means for causing the ionized isotopes tomove in a predetermined direction along said longitudinal axis and at apredetermined velocity correlated to the resonant frequency of a desiredisotope and correlated to the spacing of the spaced magnetic fields,whereby the moving ions see a variation of the magnetic field forimparting to them an energy relates to their collective resonantfrequency; and (f) means for separating the isotopes from each other onthe basis of their differential energies including a magnetic mirrordisposed along said predetermined direction.
 10. Apparatus as defined inclaim 9 wherein said means for generating spaced magnetic fields in saidcontainer provides spaced helical magnetic fields to impart additionallongitudinal motion to said ions.